Hunt for the “impossible atoms”: the quest for a tiny violation of the Pauli Exclusion Principle. Implications for physics, cosmology and philosophy.

We propose to experimentally test a major component of quantum mechanics, the Pauli Exclusion Principle (PEP), which states that two electrons cannot occupy the same quantum state.
Even though PEP represents one of the main pillars of modern physics and of our understanding of matter, life, and the Universe, it still generates many debates on possible limits of its validity. Fifty years ago Feynman wrote that not having found a simple explanation for PEP "probably means that we do not have a complete understanding of the fundamental principle involved." The quest for limits or violations of the PEP is a Big Question about the Universe.
We will perform an experimental search for "impossible atoms," i.e., atoms forbidden by PEP, using a complex, sensitive underground apparatus in Gran Sasso (Italy). We will either set very strong limits on possible PEP violation, improving the present limit by two orders of magnitude, or we will find a violation. Such a violation could be generated by non-commutativity of space variables or by the existence of extra dimensions. The framework for finding small PEP violations is based on the non-relativistic "Quon Theory" proposed by O. W. Greenberg in 1991. However, no relativistic theory exists.
The universal validity of PEP requires that two electrons are in an antisymmetric state, no matter how far they are separated. This coherence and entanglement of arbitrarily distant electrons is what Einstein called "spooky action at a distance". We will investigate the implications of tiny exceptions to PEP connected with limits on the validity of coherence and entanglement of electrons separated by a large distance.
We will explore the implications of our experimental findings for physics, cosmology, and philosophy, following a holistic approach, and will present our discoveries in 5 manuscripts for scientific peer review and in 2 articles for the general public, pursuing a deeper understanding of a main pillar of modern science.